Question 17
Alex has thought of a number $N$ in $S = \{1, 2, ..., 1001\}$, and Bibi has to find it via the following procedure. She gives Alex a list of subsets of $S$, Alex reads it and tells Bibi how many subsets in her list contain $N$. If Bibi wishes she can repeat the same with a second list, and then with a third one, but no more than 3 lists are allowed.
What least total number of subsets would enable Bibi to find $N$ with certainty?
What least total number of subsets would enable Bibi to find $N$ with certainty?